Help solving this 2d pde
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I'am trying to solve this 2d pde on 
note that in the rhs u is evaluated at 
which we can consider as a deviation 
which we can consider as a deviation where 
. I used a uniform discretization and got:
. I used a uniform discretization and got: 
As an example we can take 
and BC 
and BC I don't see how to generate the system of equations and corresponding matrix.
Any help or other method to investigate is appreciated.
回答（1 个）
Bjorn Gustavsson
2020-3-10
You are in luck! Matlab provides you with a (rather hidden) method to give you the 2-D Laplacian in matrix form. Have a look at numgrid.
qwe = delsq(numgrid('S',7));
imagesc(full(qwe))
Also have a look at delsqdemo.
For the nonlinear part you might have to look at the different iterative solvers, pcg, qmr, etc (these tools are outside of my commonly used functions...)
HTH
1 个评论
Clifford
2020-3-13
Thanks for your answer...
The l.h.s is linear so we can consider it as
where A is a matrix,
where A is a matrix, the r.h.s is nonlinear, it reads 
.
. Now we have to solve 
,
, do You think that it will be possible to solve it using matlab fsolve ?
or any more suitable numerical method (Newton method for example) ?
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